We investigate the efficiency of the two most popular frequency-domain approaches in computational electromagnetics (CEM); the finite element method (FEM) and the method of moments based on the surface integral equation (MoM/SIE), both in the context of the higher order modeling. We compare the performances of the two approaches in two simple three-dimensional (3-D) problems with similar meshes, chosen as benchmark examples. The chosen examples demonstrate full-wave analysis of a wave-guiding structure (a closed-region problem) and a scatterer in free space (an open-region problem). .